Physics Reports 454 (2007) 1–202 www.elsevier.com/locate/physrep Glueballs, hybrids, multiquarks Experimental facts versus QCD inspired concepts a, b Eberhard Klempt ∗, Alexander Zaitsev aHelmholtz-Institut für Strahlen-und Kernphysik der Rheinischen Friedrich-Wilhelms Universität, NuYallee 14-16, D–53115 Bonn, Germany bInstitute for High-Energy Physics, Moscow Region, RU-142284 Protvino, Russia Accepted 6 July 2007 Available online 26 September 2007 editor: W. Weise Abstract Glueballs, hybrids and multiquark states are predicted as bound states in models guided by quantum chromo dynamics (QCD), by QCD sum rules or QCD on a lattice. Estimates for the (scalar) glueball ground state are in the mass range from 1000 to 1800 MeV, followed by a tensor and a pseudoscalar glueball at higher mass. Experiments have reported evidence for an abundance of meson resonances with 0−+, 0++ and 2++ quantum numbers. In particular, the sector of scalar mesons is full of surprises starting from the elusive ! and " mesons. The a0(980) and f0(980), discussed extensively in the literature, are reviewed with emphasis on their Janus-like appearance as KK molecules, tetraquark states or qq mesons. Most exciting is the possibility that the three mesons ¯ ¯ f0(1370), f0(1500), and f0(1710) might reflect the appearance of a scalar glueball in the world of quarkonia. However, the existence of f0(1370) is not beyond doubt and there is evidence that both f0(1500) and f0(1710) are flavour octet states, possibly in a tetraquark composition. We suggest a scheme in which the scalar glueball is dissolved into the wide background into which all scalar flavour-singlet mesons collapse. There is an abundance of meson resonances with the quantum numbers of the #. Three states are reported below 1.5 GeV/c2 whereas quark models expect only one, perhaps two. One of these states, $(1440), was the prime glueball candidate for a long time. We show that $(1440) is the first radial excitation of the # meson. P C Hybrids may have exotic quantum numbers which are not accessible by qq mesons. There are several claims for J 1−+ exotics, some of them with properties as predicted from the flux tube model ¯interpreting the quark–antiquark binding by a=gluon string. The evidence for these states depends partly on the assumption that meson–meson interactions are dominated by s-channel resonances. Hybrids with non-exotic quantum numbers should appear as additional states. Light-quark mesons exhibit a spectrum of (squared) masses which are proportional to the sum of orbital angular momentum and radial quantum numbers. Two states do not fall under this classification. They are discussed as hybrid candidates. The concept of multiquark states has received revived interest due to new resonances in the spectrum of states with open and hidden charm. The new states are surprisingly narrow and their masses and their decay modes often do not agree with simple quark-model expectations. Lattice gauge theories have made strong claims that glueballs and hybrids should appear in the meson spectrum. However, the existence of a scalar glueball, at least with a reasonable width, is highly questionable. It is possible that hybrids will turn up in complex multibody final states even though so far, no convincing case has been made for them by experimental data. Lattice gauge ∗ Corresponding author. E-mail address: [email protected] (E. Klempt). 0370-1573/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physrep.2007.07.006 2 E. Klempt, A. Zaitsev / Physics Reports 454 (2007) 1–202 theories fail to identify the nonet of scalar mesons. Thus, at the present status of approximations, lattice gauge theories seem not to provide a trustworthy guide into unknown territory in meson spectroscopy. © 2007 Elsevier B.V. All rights reserved. PACS: 12.38. t; 12.39. x; 13.25. k; 13.75.Lb; 14.40. a − − − − Contents 1. Introduction . 5 1.1. Highlights and perspectives . 5 1.1.1. Scope of the review . 5 1.1.2. Recent outstanding achievements . 5 1.1.3. New insights . 6 1.1.4. Critique of QCD folklore . 8 1.1.5. Successes and limitations of lattice QCD . 9 1.1.6. Future options . 9 1.1.7. Hints for expert readers. 12 1.1.8. Outline . 12 1.1.9. A guide to the literature . 13 1.2. Phenomenology of qq mesons . 13 ¯ 1.2.1. The A, B, C, . of meson spectroscopy: the naming scheme . 13 1.2.2. Meson nonets . 16 1.2.3. Mixing . 16 1.2.4. The Zweig rule . 18 1.2.5. Regge trajectories . 19 1.2.6. Flavour independence of forces . 20 1.2.7. The light meson spectrum and quark model assignments . 22 2. From QCD to strong interactions . 25 2.1. Quantum chromo dynamics . 25 2.1.1. The QCD Lagrangian . 25 2.1.2. Chiral symmetry . 26 2.1.3. Instantons . 26 2.2. Chiral perturbation theory %PT . 27 2.3. Lattice QCD . 28 2.3.1. Confinement . 28 2.3.2. Glueballs . 28 2.3.3. Ground-state qq mesons . 30 ¯ 2.3.4. Hybrids . 31 2.4. QCD sum rules . 31 2.5. Flux-tube model . 32 2.6. Quark models . ..